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Euler Load given Final Deflection at Distance X from end A of Column Formula

GoEuler Load Formula

GoEuler Load given Factor of Safety Formula

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Euler load is the compressive load at which a slender column will suddenly bend or buckle. Check FAQs

P E = \frac{P}{1 - (C \cdot \frac{\sin (\frac{π \cdot x}{l})}{δ c})}

P_E - Euler Load?P - Crippling Load?C - Maximum Initial Deflection?x - Distance of Deflection from end A?l - Length of Column?δ_c - Deflection of Column?π - Archimedes' constant?

Euler Load given Final Deflection at Distance X from end A of Column Example

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Here is how the Euler Load given Final Deflection at Distance X from end A of Column equation looks like with Values.

Here is how the Euler Load given Final Deflection at Distance X from end A of Column equation looks like with Units.

Here is how the Euler Load given Final Deflection at Distance X from end A of Column equation looks like.

7.9953 = \frac{3.6}{1 - (300 \cdot \frac{\sin (\frac{3.1416 \cdot 35}{5000})}{12})}

7.9953kN = \frac{3.6kN}{1 - (300mm \cdot \frac{\sin (\frac{3.1416 \cdot 35mm}{5000mm})}{12mm})}

7.9953 = \frac{3.6}{1 - (300 \cdot \frac{\sin (\frac{3.1416 \cdot 35}{5000})}{12})}

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Euler Load given Final Deflection at Distance X from end A of Column Solution

Follow our step by step solution on how to calculate Euler Load given Final Deflection at Distance X from end A of Column?

FIRST Step Consider the formula

P E = \frac{P}{1 - (C \cdot \frac{\sin (\frac{π \cdot x}{l})}{δ c})}

Next Step Substitute values of Variables

∴

P E = \frac{3.6kN}{1 - (300mm \cdot \frac{\sin (\frac{π \cdot 35mm}{5000mm})}{12mm})}

Next Step Substitute values of Constants

∴

P E = \frac{3.6kN}{1 - (300mm \cdot \frac{\sin (\frac{3.1416 \cdot 35mm}{5000mm})}{12mm})}

Next Step Convert Units

∴

P E = \frac{3600N}{1 - (0.3m \cdot \frac{\sin (\frac{3.1416 \cdot 0.035m}{5m})}{0.012m})}

Next Step Prepare to Evaluate

∴

P E = \frac{3600}{1 - (0.3 \cdot \frac{\sin (\frac{3.1416 \cdot 0.035}{5})}{0.012})}

Next Step Evaluate

∴

P E = 7995.28104854137N

Next Step Convert to Output's Unit

∴

P E = 7.99528104854137kN

LAST Step Rounding Answer

∴

P E = 7.9953kN

Euler Load given Final Deflection at Distance X from end A of Column Formula Elements

Variables

Constants

Functions

Euler Load

Euler load is the compressive load at which a slender column will suddenly bend or buckle.

Symbol: P_E

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Euler Load

Crippling Load

Crippling Load is the load over which a column prefers to deform laterally rather than compressing itself.

Symbol: P

Measurement: ForceUnit: kN

Note: Value can be positive or negative.

Formulas to find Crippling Load

Maximum Initial Deflection

Maximum Initial Deflection is the degree to which a structural element is displaced under a load.

Symbol: C

Measurement: LengthUnit: mm

Note: Value can be positive or negative.

Formulas to find Maximum Initial Deflection

Distance of Deflection from end A

Distance of Deflection from end A is the distance x of deflection from end A.

Symbol: x

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Distance of Deflection from end A

Length of Column

Length of Column is the distance between two points where a column gets its fixity of support so its movement is restrained in all directions.

Symbol: l

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Length of Column

Deflection of Column

Deflection of Column is the displacement or bending of a column from its original, vertical position when subjected to an external load, particularly a compressive load.

Symbol: δ_c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Deflection of Column

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

Other Formulas to find Euler Load

Go Euler Load

P E = \frac{(π^{2}) \cdot ε column \cdot I}{l^{2}}

Go Euler Load given Factor of Safety

P E = \frac{P}{1 - (\frac{1}{f s})}

Go Euler Load given Maximum Deflection for Columns with Initial Curvature

P E = \frac{P}{1 - (\frac{C}{δ c})}

Other formulas in Columns With Initial Curvature category

Go Value of Distance 'X' given Initial Deflection at Distance X from end A

x = (a \sin (\frac{y'}{C})) \cdot \frac{l}{π}

Go Length of Column given Initial Deflection at Distance X from end A

l = \frac{π \cdot x}{a \sin (\frac{y'}{C})}

Go Modulus of Elasticity given Euler Load

ε column = \frac{P E \cdot (l^{2})}{(π^{2}) \cdot I}

Go Moment of Inertia given Euler Load

I = \frac{P E \cdot (l^{2})}{(π^{2}) \cdot ε column}

How to Evaluate Euler Load given Final Deflection at Distance X from end A of Column?

Euler Load given Final Deflection at Distance X from end A of Column evaluator uses Euler Load = Crippling Load/(1-(Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column)/Deflection of Column)) to evaluate the Euler Load, The Euler Load given Final Deflection at Distance X from end A of Column formula is defined as a measure of the load that a column with initial curvature can withstand, taking into account the final deflection at a specific distance from the end of the column, providing a critical value for structural integrity assessment. Euler Load is denoted by P_E symbol.

How to evaluate Euler Load given Final Deflection at Distance X from end A of Column using this online evaluator? To use this online evaluator for Euler Load given Final Deflection at Distance X from end A of Column, enter Crippling Load (P), Maximum Initial Deflection (C), Distance of Deflection from end A (x), Length of Column (l) & Deflection of Column (δ_c) and hit the calculate button.

FAQs on Euler Load given Final Deflection at Distance X from end A of Column

What is the formula to find Euler Load given Final Deflection at Distance X from end A of Column?

The formula of Euler Load given Final Deflection at Distance X from end A of Column is expressed as Euler Load = Crippling Load/(1-(Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column)/Deflection of Column)). Here is an example- 0.007995 = 3600/(1-(0.3*sin((pi*0.035)/5)/0.012)).

How to calculate Euler Load given Final Deflection at Distance X from end A of Column?

With Crippling Load (P), Maximum Initial Deflection (C), Distance of Deflection from end A (x), Length of Column (l) & Deflection of Column (δ_c) we can find Euler Load given Final Deflection at Distance X from end A of Column using the formula - Euler Load = Crippling Load/(1-(Maximum Initial Deflection*sin((pi*Distance of Deflection from end A)/Length of Column)/Deflection of Column)). This formula also uses Archimedes' constant and Sine function(s).

What are the other ways to Calculate Euler Load?

Here are the different ways to Calculate Euler Load-

Euler Load=((pi^2)*Modulus of Elasticity of Column*Moment of Inertia)/(Length of Column^2)
Euler Load=Crippling Load/(1-(1/Factor of Safety))
Euler Load=Crippling Load/(1-(Maximum Initial Deflection/Deflection of Column))

Can the Euler Load given Final Deflection at Distance X from end A of Column be negative?

Yes, the Euler Load given Final Deflection at Distance X from end A of Column, measured in Force can be negative.

Which unit is used to measure Euler Load given Final Deflection at Distance X from end A of Column?

Euler Load given Final Deflection at Distance X from end A of Column is usually measured using the Kilonewton[kN] for Force. Newton[kN], Exanewton[kN], Meganewton[kN] are the few other units in which Euler Load given Final Deflection at Distance X from end A of Column can be measured.

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Euler Load given Final Deflection at Distance X from end A of Column Formula

​GoEuler Load Formula

​GoEuler Load given Factor of Safety Formula

Euler Load given Final Deflection at Distance X from end A of Column Example

Euler Load given Final Deflection at Distance X from end A of Column Solution

Euler Load given Final Deflection at Distance X from end A of Column Formula Elements

Other Formulas to find Euler Load

Other formulas in Columns With Initial Curvature category

How to Evaluate Euler Load given Final Deflection at Distance X from end A of Column?

FAQs on Euler Load given Final Deflection at Distance X from end A of Column

Variable Name

GoEuler Load Formula

GoEuler Load given Factor of Safety Formula